Question

Please explain step by step????

Answer 1

1. A mountain biker goes for a ride in the desert. The air temperature is 21°C at the start of the ride, but the temperature in the desert will reach a peak of 51°C. The tires on the bike hold 15.6 L of nitrogen gas at a starting pressure of 249 kPa. The tires will burst when the internal pressure (Pb) reaches 269 kPa. Answer the following questions and show your work.
• How many moles of nitrogen gas are in each tire?
• What will the tire pressure be at the peak temperature in the desert?
• Will the tires burst at the peak temperature? Explain.
• To what pressure should the tire pressure be reduced before starting the ride to avoid bursting of the tires in the desert heat? (Assume no significant change in tire volume.)
Answer:

Answer 2

How many moles of nitrogen gas are in each tire?

use PV=nRT with on set of conditions (e.g. at the start of the bike ride), solve for moles, n.

Answer 3

one set*

Answer 4

how do you find that

Answer 5

find what?

Answer 6

using the formual i dont understand @aaronq

Answer 7

can you identify the parameters you need to plug into the formula?

P = pressure
V=volume
n=moles
R=constant can be found here: http://en.wikipedia.org/wiki/Gas_constant
(needs to match your pressure and volume units)
T= temp in Kelvin; T in K = 273.15 + T in Celsius

Answer 8

but i dont understand how to slove for n

Answer 9

you would solve it algebraically, you first need to determine what you're plugging into the formula.

Answer 10

got that. but what goes over what

Answer 11

rearrange the formula algebraically.

Answer 12

ab=cd \(\rightarrow a=\dfrac{cd}{b}\)

Answer 13

so would it be n= pv over rt (on bottom)

Answer 14

yes

Answer 15

is p=249kpa v=269kpa r=15.6 t=51c ?

Answer 16

im really not sure about that

Answer 17

please re-read what i posted above. R is to be found on that link, T needs to be in Kelvin, V is volume ("kPa" are units of pressure).

Answer 18

t=324.15 r= 8.31 v=15.6 p=246kpa
is that right

Answer 19

@aaronq

Answer 20

almost, you either have to use the other temp given or the other pressure given, because one set is for the start point, the other is when you're in the desert (hotter thus higher pressure).

Answer 21

so p should be 269

Answer 22

yeah, that works. now just plug it all in and solve

Answer 23

is 1.42 the answer ? thats what i got

Answer 24

yep, thats it

Answer 25

oh wait, 269 kPa is not the pressure in the desert, it's when the tire will pop.

you needed to use the first set of numbers, ill do it for you cuz it's my fault

n = [249 kPa*15.6 L]/[(21+273.15)*8.31] = 1.589 moles

Answer 26

Aw okay thank you :)

Answer 27

for "What will the tire pressure be at the peak temperature in the desert?"

use a modified version of the ideal gas equation: \(\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}\)

Answer 28

you can ignore n, R and V, for this part because they are constant throughout the problem.

Answer 29

so would it be 267kpa over 21 and 246pka over 51?

Answer 30

nope, then you'd have nothing to solve for.

you're looking for the pressure when it's 51 Celsius, so

246 and 21 are on one side and 51 and unknown pressure on the other

Remember also that the temp MUST be in Kelvin

Answer 31

so is it 246 over 294.15 and x over 324.15?

Answer 32

yes

Answer 33

is the answer 271.089

Answer 34

yes it is

Answer 35

Will the tires burst at the peak temperature? Explain.

basically if the pressure is over 269 kPa at that temp, the tires will pop.

Answer 36

and what about the last one

Answer 37

now you're using the high temp and pressure just below the bursting temp (below 269 kPa) to find what the pressure should be (not at the desert)

so use the same formula with these new numbers

Answer 38

which formula the first one you gave me?

Answer 39

and is the high temp 51

Answer 40

the formula is \(\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}\) and yes that temp

Answer 41

im confused what numbers do i use now

Answer 42

21 on the left, 268.9 kPa and 51 on the right

Answer 43

remember use Kelvin

Answer 44

i got 653.042 is that right?

Answer 45

that can't be right, the pressure should be less than the initial pressure (246 kPa)

Answer 46

i put 21 over 268.9 and 51 over X

Answer 47

it's the other way around

Answer 48

i still got the same thing :/

Answer 49

did you use Kelvin?

Answer 50

yes

Answer 51

weird, i got:

(21+273)/268.9= (51+273)/x

x=296.338

Answer 52

ohh okay